cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A072620 Permutation of natural numbers obtained from the permutation A072089 (zero-based).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 7, 8, 9, 6, 11, 12, 13, 14, 16, 28, 33, 29, 19, 30, 21, 22, 23, 20, 25, 26, 27, 15, 37, 24, 31, 38, 17, 34, 35, 36, 18, 32, 39, 40, 41, 42, 44, 47, 49, 48, 84, 112, 98, 103, 99, 85, 107, 87, 88, 56, 70, 89, 100, 90, 61, 91, 63, 64, 65, 62, 67, 68, 69, 57
Offset: 0

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Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

See the comment at A072088.

Links

Crossrefs

Compare to the plot of A070041.
A072620(n) = A072622(n+1)-1. Inverse permutation: A072619. Cf. also A072089, A070041.

A072622 Permutation of natural numbers obtained from the permutation A072089 (one-based).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 7, 12, 13, 14, 15, 17, 29, 34, 30, 20, 31, 22, 23, 24, 21, 26, 27, 28, 16, 38, 25, 32, 39, 18, 35, 36, 37, 19, 33, 40, 41, 42, 43, 45, 48, 50, 49, 85, 113, 99, 104, 100, 86, 108, 88, 89, 57, 71, 90, 101, 91, 62, 92, 64, 65, 66, 63, 68, 69, 70, 58
Offset: 1

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

See the comment at A072088.

Links

Crossrefs

A072622(n) = A072620(n-1)+1. Inverse permutation: A072621. Cf. also A070041.

A086588 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutations A072088/A072089.

Original entry on oeis.org

1, 1, 2, 5, 13, 33, 84, 204, 485, 1147, 2622, 5864, 12870
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

A086589 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutations A072088/A072089.

Original entry on oeis.org

1, 1, 2, 5, 12, 27, 60, 127, 264, 541, 1104, 2229, 4492
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

A086590 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutations A072088/A072089.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 8, 12, 45, 78, 252, 500, 2458
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

A086591 Least common multiple of cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutations A072088/A072089.

Original entry on oeis.org

1, 1, 1, 1, 2, 6, 24, 2520, 18378360, 6906955255200, 5987137029832314231356979603166508647200, 1000156941827668764767034398758639477404906113721462819980559968765060862592344000
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

A083927 Inverse function of N -> N injection A057123.

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(0)=0 because A057123(0)=0, but a(n) = 0 also for those n which do not occur as values of A057123. All positive natural numbers occur here once.
If g(n) = A083927(f(A057123(n))) then we can say that Catalan bijection g embeds into Catalan bijection f in scale n:2n, using the obvious binary tree -> general tree embedding. E.g. we have: A057163 = A083927(A057164(A057123(n))), A057117 = A083927(A072088(A057123(n))), A057118 = A083927(A072089(A057123(n))), A069770 = A083927(A072796(A057123(n))), A072797 = A083927(A072797(A057123(n))).

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Crossrefs

a(A057123(n)) = n for all n. Cf. A083925-A083926, A083928-A083929, A083935.

A057118 Permutation of natural numbers induced by the automorphism df->bf (switch from the Depth First to the Breadth First coding for the binary trees) acting on the planar binary trees encoded by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 13, 11, 12, 19, 20, 21, 14, 15, 22, 18, 16, 17, 23, 24, 27, 25, 26, 33, 34, 35, 28, 29, 36, 32, 30, 31, 51, 52, 55, 53, 54, 58, 59, 56, 37, 38, 57, 41, 39, 40, 62, 63, 64, 47, 48, 60, 49, 42, 43, 61, 50, 46, 44, 45, 65, 66, 69, 67, 68, 75, 76
Offset: 0

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Author

Antti Karttunen, Aug 11 2000

Keywords

Links

Crossrefs

Restriction of the automorphism A072089 to the plane binary trees. Being self-embeddable, this allows us also to form the permutation A070041. Inverse permutation: A057117.

A072088 Permutation of natural numbers induced by the automorphism gt-bf->df (switch from the Breadth First to the Depth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 16, 17, 18, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 33, 30, 31, 32, 29, 34, 35, 36, 37, 51, 38, 56, 60, 42, 47, 44, 45, 46, 53, 48, 49, 50, 39, 41, 43, 54, 61, 40, 57, 58, 59, 52, 55, 62, 63, 64, 65, 66, 67, 68, 69, 70, 75
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

When restricted to the subset of plane binary trees, produces the automorphism A057117, with which this shares the property of "self-embeddability": each sub-permutation of the length A000108(n): 0; 1; 2,3; 4,5,6,7,8; 9,10,11,12,13,14,19,16,17,18,15,20,21,22; 23,24,25,26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64; starts with the same cycle-structure as the previous sub-permutation. (i.e. the terms from the first to the sixth are fixed, the 7th and 11th are transposed, etc.), thus allowing us to construct the permutation A072619 (A072621).

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Crossrefs

Inverse permutation: A072089. Cf. also A014486, A057117, A072619.
Showing 1-9 of 9 results.

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